(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     47993,        981]
NotebookOptionsPosition[     47224,        956]
NotebookOutlinePosition[     47578,        972]
CellTagsIndexPosition[     47535,        969]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{"Function", " ", "definitions"}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"ck", "[", "k_", "]"}], ":=", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"4", "-", "k"}], ")"}], "*", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"5", "-", "k"}], ")"}], 
       FractionBox[
        RowBox[{"-", 
         RowBox[{"(", 
          RowBox[{"5", "-", "k"}], ")"}]}], 
        RowBox[{"(", 
         RowBox[{"4", "-", "k"}], ")"}]]]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"xsq", "[", 
      RowBox[{"r_", ",", "y_", ",", "thv_", ",", "phi_", ",", "k_"}], "]"}], ":=", 
     RowBox[{
      RowBox[{
       SuperscriptBox["y", "2"], "*", 
       SuperscriptBox[
        RowBox[{"Tan", "[", "thv", "]"}], "2"]}], "+", 
      RowBox[{"2", "*", "r", "*", "y", "*", 
       RowBox[{"Tan", "[", "thv", "]"}], "*", 
       RowBox[{"Cos", "[", "phi", "]"}]}], "+", 
      SuperscriptBox["r", "2"]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"chi", "[", 
      RowBox[{"x_", ",", "y_", ",", "k_"}], "]"}], ":=", 
     FractionBox[
      RowBox[{"y", "-", 
       RowBox[{
        RowBox[{"ck", "[", "k", "]"}], "*", "x"}]}], 
      SuperscriptBox["y", 
       RowBox[{"5", "-", "k"}]]]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", 
    RowBox[{"Constant", " ", "definitions"}], "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"TORAD", "=", 
     RowBox[{"\[Pi]", "/", "180."}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Y", "=", "0.2"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"R0", "=", "0.1"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"THV", "=", 
     RowBox[{"6.0", "*", "TORAD"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"PHI", "=", "0.0"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"K", "=", "0.0"}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", 
    RowBox[{"Solve", " ", "for", " ", 
     RowBox[{"r", "'"}]}], "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"rPrimeVals", "=", 
     RowBox[{
      RowBox[{"Solve", "[", 
       RowBox[{
        RowBox[{
         RowBox[{
          SuperscriptBox["r", "2"], "+", 
          RowBox[{"2", "*", "r", "*", "y", "*", 
           RowBox[{"Tan", "[", "thv", "]"}], "*", 
           RowBox[{"Cos", "[", "phi", "]"}]}]}], "\[Equal]", 
         RowBox[{
          SuperscriptBox["r0", "2"], "+", 
          RowBox[{"2", "*", "y", "*", "r0", "*", 
           RowBox[{"Tan", "[", "thv", "]"}]}]}]}], ",", "r"}], "]"}], "//", 
      "Simplify"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"rPrimePlus", "[", 
      RowBox[{
      "rVal_", ",", "yVal_", ",", "tVal_", ",", "pVal_", ",", "kVal_"}], 
      "]"}], ":=", 
     RowBox[{
      RowBox[{"rPrimeVals", "[", 
       RowBox[{"[", "1", "]"}], "]"}], "/.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"r0", "\[Rule]", "rVal"}], ",", 
        RowBox[{"y", "\[Rule]", "yVal"}], ",", 
        RowBox[{"thv", "\[Rule]", "tVal"}], ",", 
        RowBox[{"phi", "\[Rule]", "pVal"}], ",", 
        RowBox[{"k", "\[Rule]", "kVal"}]}], "}"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"rPrimeMinus", "[", 
      RowBox[{
      "rVal_", ",", "yVal_", ",", "tVal_", ",", "pVal_", ",", "kVal_"}], 
      "]"}], ":=", 
     RowBox[{
      RowBox[{"rPrimeVals", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "/.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"r0", "\[Rule]", "rVal"}], ",", 
        RowBox[{"y", "\[Rule]", "yVal"}], ",", 
        RowBox[{"thv", "\[Rule]", "tVal"}], ",", 
        RowBox[{"phi", "\[Rule]", "pVal"}], ",", 
        RowBox[{"k", "\[Rule]", "kVal"}]}], "}"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"rPrime", "[", 
      RowBox[{
      "rVal_", ",", "yVal_", ",", "tVal_", ",", "pVal_", ",", "kVal_"}], 
      "]"}], ":=", 
     RowBox[{
      RowBox[{"rPrimeVals", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "/.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"r0", "\[Rule]", "rVal"}], ",", 
        RowBox[{"y", "\[Rule]", "yVal"}], ",", 
        RowBox[{"thv", "\[Rule]", "tVal"}], ",", 
        RowBox[{"phi", "\[Rule]", "pVal"}], ",", 
        RowBox[{"k", "\[Rule]", "kVal"}]}], "}"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"PhiIntegrand", "[", 
      RowBox[{
      "rVal_", ",", "yVal_", ",", "tVal_", ",", "pVal_", ",", "kVal_"}], 
      "]"}], ":=", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"r", "/", "rVal"}], ")"}], "2"], "/.", 
      RowBox[{"rPrime", "[", 
       RowBox[{"rVal", ",", "yVal", ",", "tVal", ",", "pVal", ",", "kVal"}], 
       "]"}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"PhiInt", "[", 
      RowBox[{"rVal_", ",", "yVal_", ",", "tVal_", ",", "kVal_"}], "]"}], ":=", 
     RowBox[{"NIntegrate", "[", 
      RowBox[{
       RowBox[{"PhiIntegrand", "[", 
        RowBox[{"rVal", ",", "yVal", ",", "tVal", ",", "phi", ",", "kVal"}], 
        "]"}], ",", 
       RowBox[{"{", 
        RowBox[{"phi", ",", "0", ",", 
         RowBox[{"2", "*", "\[Pi]"}]}], "}"}]}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"r", "/.", 
        RowBox[{"rPrimeMinus", "[", 
         RowBox[{"R0", ",", "Y", ",", "THV", ",", "phi", ",", "K"}], "]"}]}], 
       ",", 
       RowBox[{"r", "/.", 
        RowBox[{"rPrimePlus", "[", 
         RowBox[{"R0", ",", "Y", ",", "THV", ",", "phi", ",", "K"}], 
         "]"}]}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"phi", ",", "0", ",", 
       RowBox[{"2", "*", "\[Pi]"}]}], "}"}], ",", 
     RowBox[{"PlotLegends", "\[Rule]", "\"\<Expressions\>\""}]}], "]"}], 
   "\[IndentingNewLine]", 
   RowBox[{"rPrimeMinus", "[", 
    RowBox[{"r0", ",", "y", ",", "thv", ",", "phi", ",", "k"}], "]"}], 
   "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{"(*", "Plotting", "*)"}], "\[IndentingNewLine]", 
   RowBox[{"Manipulate", "[", 
    RowBox[{
     RowBox[{"Plot", "[", 
      RowBox[{
       RowBox[{"PhiInt", "[", 
        RowBox[{"r0", ",", "y", ",", 
         RowBox[{"thv", "*", "TORAD"}], ",", "0.0"}], "]"}], ",", 
       RowBox[{"{", 
        RowBox[{"r0", ",", "0.0", ",", "1.0"}], "}"}]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", "0.0", ",", "1.0", ",", "0.1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"thv", ",", "0.0", ",", "10.0", ",", "1.0"}], "}"}]}], "]"}], 
   "\[IndentingNewLine]", 
   RowBox[{"Manipulate", "[", 
    RowBox[{
     RowBox[{"Plot", "[", 
      RowBox[{
       RowBox[{"PhiIntegrand", "[", 
        RowBox[{"R0", ",", "Y", ",", "THV", ",", "phi", ",", "K"}], "]"}], 
       ",", 
       RowBox[{"{", 
        RowBox[{"phi", ",", "0", ",", 
         RowBox[{"2", "*", "\[Pi]"}]}], "}"}]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"THV", ",", "0.0", ",", 
       RowBox[{"15.0", "*", "TORAD"}], ",", 
       RowBox[{"0.01", "*", "TORAD"}]}], "}"}]}], "]"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Manipulate", "[", 
     RowBox[{
      RowBox[{"Plot", "[", 
       RowBox[{
        RowBox[{"PhiInt", "[", 
         RowBox[{"r0", ",", "Y", ",", "thv", ",", "K"}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"r0", ",", "0.0", ",", "0.5"}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"thv", ",", "0.0", ",", 
        RowBox[{"15.0", "*", "TORAD"}], ",", 
        RowBox[{"0.01", "*", "TORAD"}]}], "}"}]}], "]"}], ";"}]}]}]], "Input",\

 CellChangeTimes->{{3.713537747083359*^9, 3.713537996802779*^9}, {
   3.7135389215512114`*^9, 3.713539087774581*^9}, {3.71353920338682*^9, 
   3.713539231074785*^9}, {3.713539292067463*^9, 3.713539344854072*^9}, {
   3.7135393765855217`*^9, 3.713539430815536*^9}, {3.713539470838838*^9, 
   3.713539551175746*^9}, {3.713539581247712*^9, 3.713539582182865*^9}, {
   3.71353961445947*^9, 3.7135396678491087`*^9}, {3.7135397367531557`*^9, 
   3.713539768126934*^9}, {3.7135398024670963`*^9, 3.713539837444519*^9}, {
   3.713539878643712*^9, 3.713539924896962*^9}, {3.7135403785653553`*^9, 
   3.7135404069807243`*^9}, {3.71354049434503*^9, 3.7135404950920143`*^9}, 
   3.713540595126895*^9, {3.7135406867222147`*^9, 3.713540764544712*^9}, 
   3.713540825986899*^9, {3.71354085662564*^9, 3.713540950767169*^9}, {
   3.713615253230813*^9, 3.713615268913686*^9}, {3.7136153074299583`*^9, 
   3.713615351827355*^9}, {3.7136154407394447`*^9, 3.7136155088541517`*^9}, {
   3.7136194972390213`*^9, 3.713619543392046*^9}, {3.713620002651017*^9, 
   3.713620007534153*^9}, {3.713620189548587*^9, 3.713620441386363*^9}, {
   3.713620474777375*^9, 3.713620651848235*^9}, {3.713620730766341*^9, 
   3.7136207967832813`*^9}, {3.713620833118223*^9, 3.713620924457836*^9}, {
   3.713621142501461*^9, 3.7136211768076563`*^9}, {3.713621231222637*^9, 
   3.71362127768958*^9}, {3.713621346221521*^9, 3.713621377402816*^9}, {
   3.713623215257922*^9, 3.713623291298723*^9}, {3.713623323629171*^9, 
   3.713623426083785*^9}, {3.713623465858754*^9, 3.713623542201144*^9}, {
   3.713623601853559*^9, 3.713623620929105*^9}, 3.713623676401689*^9, {
   3.7136237120287*^9, 3.713623846777961*^9}, {3.713623878281248*^9, 
   3.713624212215041*^9}, {3.7136242458688173`*^9, 3.713624257089101*^9}, {
   3.713624292848971*^9, 3.713624345294949*^9}, {3.713624386798422*^9, 
   3.713624447591351*^9}, 3.713626261598672*^9, {3.713626932569696*^9, 
   3.7136269466643267`*^9}, {3.713626978752102*^9, 
   3.713627152599989*^9}},ExpressionUUID->"ae9aa301-dedf-41f3-a22d-\
2f0ffcd0ef2f"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{{{}, {}, 
       TagBox[{
         Directive[
          Opacity[1.], 
          RGBColor[0.368417, 0.506779, 0.709798], 
          AbsoluteThickness[1.6]], 
         LineBox[CompressedData["
1:eJw12Xk4lF0bAHD7zNjKPoMiqUSpLFGW+06L0CtkKSIpKkUo6i2KFrRJtiJb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          "]]}, Annotation[#, "Charting`Private`Tag$76147#1"]& ], 
       TagBox[{
         Directive[
          Opacity[1.], 
          RGBColor[0.880722, 0.611041, 0.142051], 
          AbsoluteThickness[1.6]], 
         LineBox[CompressedData["
1:eJw12Xk4lF0bAHDrmLFkN2MvSppKhVKh504ilLJEiCRbtlBRIZW9vF4kRdZk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          "]]}, 
        Annotation[#, "Charting`Private`Tag$76147#2"]& ]}}, {}, {}}, {
    DisplayFunction -> Identity, Ticks -> {Automatic, Automatic}, 
     AxesOrigin -> {0, 0}, FrameTicks -> {{Automatic, 
        Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
        Charting`ScaledFrameTicks[{Identity, Identity}]}}, 
     GridLines -> {None, None}, DisplayFunction -> Identity, 
     PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
     DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> 
     Identity, Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], 
     Method -> {
      "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
       AbsolutePointSize[6], "ScalingFunctions" -> None, 
       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& )}}, PlotRange -> 
     NCache[{{0, 2 Pi}, {-0.1420416941062704, 0.1420416912214419}}, {{
        0, 6.283185307179586}, {-0.1420416941062704, 0.1420416912214419}}], 
     PlotRangeClipping -> True, PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{
       RowBox[{"r", "/.", "\[VeryThinSpace]", 
         RowBox[{"rPrimeMinus", "(", 
           RowBox[{"R0", ",", "Y", ",", "THV", ",", "phi", ",", "K"}], 
           ")"}]}], 
       RowBox[{"r", "/.", "\[VeryThinSpace]", 
         RowBox[{"rPrimePlus", "(", 
           RowBox[{"R0", ",", "Y", ",", "THV", ",", "phi", ",", "K"}], 
           ")"}]}]}, "LineLegend", DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    RGBColor[0.368417, 0.506779, 0.709798], 
                    AbsoluteThickness[1.6]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    RGBColor[0.368417, 0.506779, 0.709798], 
                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    RGBColor[0.880722, 0.611041, 0.142051], 
                    AbsoluteThickness[1.6]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    RGBColor[0.880722, 0.611041, 0.142051], 
                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"LineLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0.368417, 0.506779, 0.709798], 
                    RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> 
                    True, FrameStyle -> 
                    RGBColor[
                    0.24561133333333335`, 0.3378526666666667, 
                    0.4731986666666667], FrameTicks -> None, PlotRangePadding -> 
                    None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    "RGBColor[0.368417, 0.506779, 0.709798]"], Appearance -> 
                    None, BaseStyle -> {}, BaselinePosition -> Baseline, 
                    DefaultBaseStyle -> {}, ButtonFunction :> 
                    With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0.368417, 0.506779, 0.709798]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
                     Selectable -> False], ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], 
               ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0.880722, 0.611041, 0.142051], 
                    RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> 
                    True, FrameStyle -> 
                    RGBColor[
                    0.587148, 0.40736066666666665`, 0.09470066666666668], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    "RGBColor[0.880722, 0.611041, 0.142051]"], Appearance -> 
                    None, BaseStyle -> {}, BaselinePosition -> Baseline, 
                    DefaultBaseStyle -> {}, ButtonFunction :> 
                    With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0.880722, 0.611041, 0.142051]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
                     Selectable -> False], ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}]}],
              "}"}], ",", 
           RowBox[{"{", 
             RowBox[{
               TagBox[#, HoldForm], ",", 
               TagBox[#2, HoldForm]}], "}"}], ",", 
           RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
      Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{{3.713620415747411*^9, 3.713620442504671*^9}, {
   3.713620523281066*^9, 3.7136206525351973`*^9}, {3.7136207370641727`*^9, 
   3.713620766671062*^9}, 3.713620874801011*^9, {3.7136209182018023`*^9, 
   3.7136209250117607`*^9}, 3.713621178062557*^9, 3.7136212786233387`*^9, 
   3.713621378918354*^9, 3.7136232938093977`*^9, 3.7136233787391787`*^9, 
   3.7136234322658167`*^9, {3.713623520889592*^9, 3.7136235433450813`*^9}, 
   3.713623630538034*^9, {3.713623820482957*^9, 3.7136238473511868`*^9}, 
   3.713623883295681*^9, 3.713623924075506*^9, {3.7136239802590637`*^9, 
   3.7136240371515207`*^9}, 3.713624080789016*^9, 3.713624131348322*^9, 
   3.713624213918869*^9, 3.7136242610599833`*^9, {3.713624303594491*^9, 
   3.7136243469609337`*^9}, {3.7136243880940113`*^9, 3.713624398272496*^9}, {
   3.713624435647189*^9, 3.713624450478767*^9}, 3.7136249469357433`*^9, 
   3.713626264746457*^9, {3.713626934981943*^9, 3.713626947742559*^9}, {
   3.713627060562832*^9, 3.713627116422501*^9}, {3.7136271480472927`*^9, 
   3.713627153960966*^9}},ExpressionUUID->"1353acf5-84de-40bd-9ac9-\
78b78ccc045b"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"r", "\[Rule]", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "y"}], " ", 
     RowBox[{"Cos", "[", "phi", "]"}], " ", 
     RowBox[{"Tan", "[", "thv", "]"}]}], "+", 
    SqrtBox[
     RowBox[{
      SuperscriptBox["r0", "2"], "+", 
      RowBox[{"2", " ", "r0", " ", "y", " ", 
       RowBox[{"Tan", "[", "thv", "]"}]}], "+", 
      RowBox[{
       SuperscriptBox["y", "2"], " ", 
       SuperscriptBox[
        RowBox[{"Cos", "[", "phi", "]"}], "2"], " ", 
       SuperscriptBox[
        RowBox[{"Tan", "[", "thv", "]"}], "2"]}]}]]}]}], "}"}]], "Output",
 CellChangeTimes->{{3.713620415747411*^9, 3.713620442504671*^9}, {
   3.713620523281066*^9, 3.7136206525351973`*^9}, {3.7136207370641727`*^9, 
   3.713620766671062*^9}, 3.713620874801011*^9, {3.7136209182018023`*^9, 
   3.7136209250117607`*^9}, 3.713621178062557*^9, 3.7136212786233387`*^9, 
   3.713621378918354*^9, 3.7136232938093977`*^9, 3.7136233787391787`*^9, 
   3.7136234322658167`*^9, {3.713623520889592*^9, 3.7136235433450813`*^9}, 
   3.713623630538034*^9, {3.713623820482957*^9, 3.7136238473511868`*^9}, 
   3.713623883295681*^9, 3.713623924075506*^9, {3.7136239802590637`*^9, 
   3.7136240371515207`*^9}, 3.713624080789016*^9, 3.713624131348322*^9, 
   3.713624213918869*^9, 3.7136242610599833`*^9, {3.713624303594491*^9, 
   3.7136243469609337`*^9}, {3.7136243880940113`*^9, 3.713624398272496*^9}, {
   3.713624435647189*^9, 3.713624450478767*^9}, 3.7136249469357433`*^9, 
   3.713626264746457*^9, {3.713626934981943*^9, 3.713626947742559*^9}, {
   3.713627060562832*^9, 3.713627116422501*^9}, {3.7136271480472927`*^9, 
   3.7136271539786777`*^9}},ExpressionUUID->"bf4bf1ac-572d-46c2-bdef-\
a0995794b825"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`thv$$ = 0., $CellContext`y$$ = 0., 
    Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`y$$], 0., 1., 0.1}, {
      Hold[$CellContext`thv$$], 0., 10., 1.}}, Typeset`size$$ = {
    360., {107., 112.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`y$76206$$ = 
    0, $CellContext`thv$76207$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`thv$$ = 0., $CellContext`y$$ = 0.}, 
      "ControllerVariables" :> {
        Hold[$CellContext`y$$, $CellContext`y$76206$$, 0], 
        Hold[$CellContext`thv$$, $CellContext`thv$76207$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Plot[
        $CellContext`PhiInt[$CellContext`r0, $CellContext`y$$, \
$CellContext`thv$$ $CellContext`TORAD, 0.], {$CellContext`r0, 0., 1.}], 
      "Specifications" :> {{$CellContext`y$$, 0., 1., 
         0.1}, {$CellContext`thv$$, 0., 10., 1.}}, "Options" :> {}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{405., {166., 172.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{{3.713620415747411*^9, 3.713620442504671*^9}, {
   3.713620523281066*^9, 3.7136206525351973`*^9}, {3.7136207370641727`*^9, 
   3.713620766671062*^9}, 3.713620874801011*^9, {3.7136209182018023`*^9, 
   3.7136209250117607`*^9}, 3.713621178062557*^9, 3.7136212786233387`*^9, 
   3.713621378918354*^9, 3.7136232938093977`*^9, 3.7136233787391787`*^9, 
   3.7136234322658167`*^9, {3.713623520889592*^9, 3.7136235433450813`*^9}, 
   3.713623630538034*^9, {3.713623820482957*^9, 3.7136238473511868`*^9}, 
   3.713623883295681*^9, 3.713623924075506*^9, {3.7136239802590637`*^9, 
   3.7136240371515207`*^9}, 3.713624080789016*^9, 3.713624131348322*^9, 
   3.713624213918869*^9, 3.7136242610599833`*^9, {3.713624303594491*^9, 
   3.7136243469609337`*^9}, {3.7136243880940113`*^9, 3.713624398272496*^9}, {
   3.713624435647189*^9, 3.713624450478767*^9}, 3.7136249469357433`*^9, 
   3.713626264746457*^9, {3.713626934981943*^9, 3.713626947742559*^9}, {
   3.713627060562832*^9, 3.713627116422501*^9}, {3.7136271480472927`*^9, 
   3.713627154026658*^9}},ExpressionUUID->"844acc5f-6f60-4041-9f15-\
ea3aacc52840"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`THV$$ = 0., Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`THV$$], 0., 0.2617993877991494, 
      0.00017453292519943296`}}, Typeset`size$$ = {360., {109., 113.}}, 
    Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = 
    True, $CellContext`THV$76236$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, "Variables" :> {$CellContext`THV$$ = 0.}, 
      "ControllerVariables" :> {
        Hold[$CellContext`THV$$, $CellContext`THV$76236$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Plot[
        $CellContext`PhiIntegrand[$CellContext`R0, $CellContext`Y, \
$CellContext`THV$$, $CellContext`phi, K], {$CellContext`phi, 0, 2 Pi}], 
      "Specifications" :> {{$CellContext`THV$$, 0., 0.2617993877991494, 
         0.00017453292519943296`}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{405., {154., 160.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{{3.713620415747411*^9, 3.713620442504671*^9}, {
   3.713620523281066*^9, 3.7136206525351973`*^9}, {3.7136207370641727`*^9, 
   3.713620766671062*^9}, 3.713620874801011*^9, {3.7136209182018023`*^9, 
   3.7136209250117607`*^9}, 3.713621178062557*^9, 3.7136212786233387`*^9, 
   3.713621378918354*^9, 3.7136232938093977`*^9, 3.7136233787391787`*^9, 
   3.7136234322658167`*^9, {3.713623520889592*^9, 3.7136235433450813`*^9}, 
   3.713623630538034*^9, {3.713623820482957*^9, 3.7136238473511868`*^9}, 
   3.713623883295681*^9, 3.713623924075506*^9, {3.7136239802590637`*^9, 
   3.7136240371515207`*^9}, 3.713624080789016*^9, 3.713624131348322*^9, 
   3.713624213918869*^9, 3.7136242610599833`*^9, {3.713624303594491*^9, 
   3.7136243469609337`*^9}, {3.7136243880940113`*^9, 3.713624398272496*^9}, {
   3.713624435647189*^9, 3.713624450478767*^9}, 3.7136249469357433`*^9, 
   3.713626264746457*^9, {3.713626934981943*^9, 3.713626947742559*^9}, {
   3.713627060562832*^9, 3.713627116422501*^9}, {3.7136271480472927`*^9, 
   3.713627154197256*^9}},ExpressionUUID->"2d3236ef-187f-4e95-a937-\
e6fb81d1e100"]
}, Open  ]]
},
WindowSize->{1302, 848},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"11.1 for Mac OS X x86 (32-bit, 64-bit Kernel) (April 27, \
2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 9795, 249, 618, "Input", "ExpressionUUID" -> \
"ae9aa301-dedf-41f3-a22d-2f0ffcd0ef2f"],
Cell[10378, 273, 29242, 536, 229, "Output", "ExpressionUUID" -> \
"1353acf5-84de-40bd-9ac9-78b78ccc045b"],
Cell[39623, 811, 1712, 34, 43, "Output", "ExpressionUUID" -> \
"bf4bf1ac-572d-46c2-bdef-a0995794b825"],
Cell[41338, 847, 3008, 54, 355, "Output", "ExpressionUUID" -> \
"844acc5f-6f60-4041-9f15-ea3aacc52840"],
Cell[44349, 903, 2859, 50, 331, "Output", "ExpressionUUID" -> \
"2d3236ef-187f-4e95-a937-e6fb81d1e100"]
}, Open  ]]
}
]
*)

